The attack occurred during a fight, Rosenthal said, but the murder was premeditated.

''Garcia brought the knife and the machete for the sole purpose of killing the mother,'' he said.

A neighbor, Paul Butler, who heard the attack said, ''They frequently had these arguments, and I thought this was just another argument.''

Rosenthal said Mrs. Lomax, a receptionist for an investment banking company, came home May 24 and found Garcia with her daughter.

Mrs. Lomax had objected from the start to the 18-month romance and in the argument that followed the daughter picked up ''a Rambo knife, 10 inches long with a six-inch blade, and stabbed her mother in the back,'' said Rosenthal.

''At one point the mother ran to the front door, opened the door and her neighbor saw her fingers and heard her screaming. They pulled her back in and they continued to hack at her and when the neighbor said 'What's going on?' the daughter screamed, 'We're having a fight - leave us alone,' '' the chief said.

''In the course of hacking at the body, he with the machete and she with the Rambo knife, they each cut the other. He required 10 to 12 stitches and she required six stitches.''

The couple went from the apartment to the home of Garcia's relatives, where they explained their bleeding by saying they had just been wounded fighting off would-be robbers in the park.

After being sewn up at a hospital, police took them to the Seventh Precinct station to look at mug shots and try to identify their ''attackers.''

The next day, the girl called her mother's office to report her ill. After trying several times to reach her by telephone, Mrs. Lomax's employers got in touch with Housing Authority police, who discovered the body Thursday morning.

Garcia and Miss Williams were arrested that night near his East Village home.

Miss Williams, whom Rosenthal said was being charged as an adult, was the youngest of Mrs. Lomax's six children and the last still living with her.